Color (Greek)
Gamma decay — the third-order Greek measuring how your gamma estimate drifts overnight from time passing alone, before the market even opens.
Definition
Color, also called gamma decay or gamma-theta, is a third-order option Greek that measures the rate at which an option's gamma changes purely from the passage of time, with the underlying price and implied volatility held fixed. It is mathematically the partial derivative of gamma with respect to time, and equivalently the third-order mixed partial of option value with respect to the underlying price twice and time once. Just as charm tells you how delta bleeds overnight, color tells you how gamma bleeds overnight — the convexity of your position is not constant from one trading day to the next, even in a completely static market.
Why it matters
Understanding color becomes non-negotiable for professional options desks and systematic traders who gamma-hedge their books on NSE's weekly expiry cycles. In the final three to five trading sessions before a Nifty, Bank Nifty, Fin Nifty, or Midcap Nifty weekly expiry, at-the-money gamma spikes dramatically — this is well known. What is less appreciated is that gamma's value on expiry morning is not predictable from the prior evening's gamma reading unless color is accounted for. A position with gamma of 0.06 at Tuesday's close, and a color of +0.015 per day, will have gamma of approximately 0.075 by Wednesday's open even if Nifty hasn't moved and implied volatility hasn't shifted. For a trader with 5,000 lots long, that 0.015 gamma increment means an additional 75 lots of delta sensitivity per Nifty point — a hedge rebalancing requirement of real consequence that would be missed entirely if the desk relied on yesterday's gamma figure. Color is also relevant for market makers pricing the overnight theta on their books, since the gamma risk profile they carry into the next session is materially different from when they closed. In India's market structure, where retail activity surges in the last hour of weekly expiry sessions, large OI concentration at ATM strikes creates gamma and color spikes that can amplify intraday volatility — a well-documented empirical pattern.
Formula
Color is defined as:
Color = ∂Γ / ∂t
Under the Black-Scholes model for a non-dividend-paying underlying:
Color = − N'(d1) / (2Sσ√T) × [2rT + 1 − d1d2 / (2T)]
where N'(d1) is the standard normal probability density function evaluated at d1, S is the underlying spot price, σ is implied volatility, T is time to expiry in years, r is the risk-free rate, and d1, d2 are the standard Black-Scholes terms. Color is typically quoted as the change in gamma per calendar day — a color of +0.002 means gamma increases by 0.002 each passing day even with no market movement.
Example
Suppose a hypothetical Nifty 23,500 CE has 3 days to expiry and a gamma of 0.07 on Monday evening. Its color is +0.01 per day. Overnight, Nifty stays flat. On Tuesday morning, gamma has drifted to approximately 0.08. A delta-hedged position that was correctly neutralised Monday evening now carries an additional 0.01 units of gamma per lot — meaning for each Nifty point moved on Tuesday, the delta will shift 0.01 more than the Monday hedge assumed. Across 2,000 long calls, this is an unplanned 20-lot delta move per Nifty point, which the trader must rebalance before the market opens if they want to maintain their intended risk profile. These numbers are illustrative only and not a recommendation.
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